For the cross badmephisto has an excellent video
https://www.youtube.com/watch?v=hY_FbpdNRCQ
One of the things that really helps with seeing the whole cross is learning more ways to insert two cross pieces together instead of one by one.
An example I recently learned was that if you set up the cube with F’ R u’ R U with cross color on bottom, then the inverse of that U' R' u R' F is very fast and for me it is faster than other ways of solving those remaining 2 cross pieces. And since then I have had solves where I could easily insert the first 2 cross pieces and get this similar pattern and while still in inspection I can tell myself to put that last cross piece in the back and do R' u R' F.
For finding pairs in F2L it really just comes from practice. The more you practice the more you can recognize pairs quickly and you will eventually be able to subconsciously know where you should be looking for the pairs.
When I play around with the idea of being color neutral I have a hard time finding pairs. Much more than with my normal cross color. I know where I should be looking but I just can't recognize the pairs as fast as I can with what I am used to. The only difference is that I have had more practice solving on green and blue than other colors. So I say just keep practicing and focus on trying to find the pairs and one day you will notice you are getting better and better and that is when you start beating your personal bests.
One thing I noticed is that I subconsciously block out pieces with blue when I solve a green cross. When solving a green cross I see a red and yellow edge and know that that is one of the pieces I am looking for. When I solve on a white cross (which is unfamiliar to me) I can't tell the difference between the importance of a green-orange edge and a green-yellow edge while in a normal solve. The only way to recognize the difference quicker is to get more experience with it.
So one thing you can try is to mentally block out pieces that are opposite of the cross you are solving and you might be able to better filter where the F2L pieces are.
So in short the more you practice the more you will be familiar with these parts of the solve overtime.